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New York University - ECON UA.31 

 

Urban Economics

 

Problem Set #3 due Tuesday, Apr 5, in class

 

 

1. The third largest city of a country has a population of 2.5 million. Using the ranksize rule, what is the population of the 10^th largest city? 

 

 

 

 

2. Assume an urban cluster’s income (I) is given by the function I=4N, where N denotes the cluster’s population in million. The cluster’s diseconomies of aggregation (C) are given by C=0.5N². 
   1. Calculate the city’s utility maximizing population. 
   2. At this population, how large is the resulting utility? 
   3. Calculate the resulting utility if the population were on million higher and one million lower than the optimum. 

 

 

3. Assume the utility functions for two cities are identical and are given by  U=N - 0.1*N², where N denotes the city’s population in million. 
   1. What is each city’s utility maximizing population?
   2. If each city had a population of 6.5 million people, how would these cities change their size? Assuming that the total population of 13 million cannot be changed, would there be a smaller and a larger city? Would there be three or more cities? Or would there be no change at all. Explain.